Surface Shape Measurement Device and Surface Shape Measurement Method

ABSTRACT

The present invention provides a surface shape measuring device and a surface shape measuring method which do not require a physical reference plane and can improve measurement accuracy without using a mechanical adjustment mechanism. The illumination light condensing point PQ and the reference light condensing point PL are arranged as mirror images of each other with respect to the virtual plane VP, and each data of the object light O, being a reflected light of the spherical wave illumination light Q, and the inline spherical wave reference light L is recorded on each hologram. On the virtual plane VP, the reconstructed object light hologram hV for measurement is generated, and the spherical wave optical hologram sV representing a spherical wave light emitted from the reference light condensing point PL is analytically generated. The height distribution of the surface to be measured of the object 4 is obtained from the phase distribution obtained by dividing the reconstructed object light hologram hV by the spherical wave light hologram sV. High-accuracy surface shape measurement without requiring a reference plane such as a glass substrate is realized by comparing the phase data of the reflected light acquired from the surface to be measured and the phase distribution on the plane cut surface of the spherical wave obtained analytically.

TECHNICAL FIELD

The present invention relates to a surface shape measuring device and asurface shape measuring method in digital holography.

BACKGROUND ART

Conventionally, as a technology for analyzing light waves such asreflected light and transmitted light, there is holography by which dataof light intensity and phase are recorded together, on a recordingmedium such as a photographic plate called a hologram, and analyzed. Inrecent years, holography has been performed to acquire the intensity andphase of a light wave as digital data using an image sensor and asemiconductor memory or to generate a hologram on a computer foranalysis. Such holography is called digital holography.

In the digital holography, various technologies have been proposed forachieving higher speed and higher accuracy in hologram data acquisitionand processing, and have been applied to imaging. For example, digitalholography is known in which spatial frequency filtering and spatialheterodyne modulation are applied to hologram data recorded by one shot,and a complex amplitude inline hologram for object image reconstructionis generated quickly and accurately (for example, patent document 1).

In order to solve the problem of the conventional optical microscope, amethod for accurately acquiring object light of a large numericalaperture by one shot using holography without using any imaging lens anda method for accurately reconstructing high resolution three-dimensionalimage on a computer are known (for example, patent document 2).According to these method, a lens less three-dimensional microscope isrealized, and such a microscope is capable of acquiring andreconstructing an undistorted high-resolution three-dimensional movingimage. Since such a microscope does not use any imaging lens, it ispossible to solve the problem of the conventional optical microscope,namely, the problem caused by the influence of the medium and theimaging lens.

Moreover, there is known a high resolution tomography, which uses areflection type lens less holographic microscope and wavelength sweeplaser light, for measuring the cell in culture solution or the structurein a living body tissue with high resolution (for example, patentdocuments 3).

Furthermore, there is known a method for reconstructing an object lightwith a condition of a synthetic numerical aperture exceeding 1, bysynthesizing a plurality of large numerical aperture object lightholograms in which object lights of large numerical aperture arerecorded as hologram data for each incident angle of illumination light,wherein the object lights are emitted lights from an object illuminatedwith illumination lights having different incident directions (forexample, patent document 4). According to this method, an ultra-highresolution three-dimensional microscope having a resolution exceedingusual diffraction limit can be realized.

In addition, there is known a holographic ellipsometry device that usesaccurate recording of light waves by one-shot digital holography andplane wave expansion of recorded light waves (for example, see patentdocument 5). According to this ellipsometry device, since data ofreflected lights of non-parallel illumination lights having a largenumber of incident angles are collectively recorded in one hologram, theellipsometry can be performed for each of a large number of wave numbervectors corresponding to the incident angle in order to obtain theellipsometric angles LP and A, and the measurement efficiency can beimproved.

Further, an interferometric measuring device for performing shapemeasurement is known, in which an image pickup device, two imaginglenses, a cube-type beam splitter, an element having a Fizeau referenceplane, and an object to be measured are arranged in series, andinterference fringes of lights reflected, respectively from thereference plane and the object to be measured, are recorded (forexample, see patent document 6).

PRIOR ART DOCUMENTS Patent Documents

-   Patent document 1: WO2011/089820-   Patent document 2: WO2012/005315-   Patent document 3: WO2014/054776-   Patent document 4: WO2015/064088-   Patent document 5: WO2018/038064-   Patent document 6: U.S. Pat. No. 8,269,981

DISCLOSURE OF THE INVENTION

The holography as shown in patent documents 1 to 5 described above canbe applied to microscopic observation and/or shape measurement of arelatively small area, however, a technology capable of large areameasurement is desired, for example, a technology applicable to flatnessmeasurement and/or surface measurement of a semiconductor wafer whosediameter is increasing. Further, the interference measuring device asshown in patent document 6 described above uses Fizeau interferencewhich is a general method for flatness measurement, however, due to theusage of the reference plane, there are following problems inherent inthe Fizeau interference measuring device or Fizeau interferometer.

Fizeau interferometer is considered to be one of the most accurate andhigh-speed flatness measurement devices, and has been adopted as aflatness measurement device in standard equipment laboratories invarious countries. In Fizeau interferometry, interference fringes,created between a light reflected by a reference plane of a transparentglass plate that serves as a standard plane and a light reflected by anobject surface to be measured, are recorded in a hologram. To improvethe measurement accuracy, the reference plane is moved slightly in thenormal direction thereof to shift the phase of the interference fringes,and multiple set of interference fringes with different phases arerecorded in multiple holograms and used to analyze the plane shape ofthe surface to be measured. The measurement result thus obtained isinevitably a comparison between the reference plane and the surface tobe measured, and absolute shape correction of the reference plane isnecessary to obtain an absolute value of the flatness. The three-sheetalignment method is used for the absolute shape correction.

The optical system of the Fizeau interferometer has a relatively smallnumber of optical components and a simple structure in principle,however, practically, a tilt adjustment and/or vertical movementmechanism and a turntable for absolute shape measurement correction ofthe object to be measured are required in addition to the referenceplane that serve as the measurement reference and collimating lens. Theaccuracy of the measurement is affected by the uncertainty of thereference plane shape correction, the uncertainty of the phase shift,and the uncertainty due to environmental fluctuations. It is difficultto suppress the combined measurement uncertainty to 10 nm or less. Asanother problem, since the reference plane and the collimating lens areused, the dimension of the measurable object is limited to about 300 mmor less, and it is difficult to increase the diameter beyond that.Further, there is a problem that the contrast of the interferencefringes is lowered for the surface to be measured having a reflectancegreatly different from that of the reference plane made of glass, andthis makes it difficult to perform highly accurate measurement.

The present invention is to solve the above-mentioned problems, and itis an object of the present invention to provide a surface shapemeasuring device and a surface shape measuring method which can improvemeasurement accuracy by a simple configuration without requiring aphysical reference plane as a comparison standard of flatness and alsowithout using a mechanical adjustment mechanism,

In order to attain the above-mentioned subject, the surface shapemeasuring device using holography of the present invention, comprises:

a data acquisition unit for acquiring data of an object light (O) thatis a reflected light of a spherical wave illumination light (Q)illuminating a surface to be measured and data of an inline sphericalwave reference light (L) that is inline with respect to the object light(O), respectively, as an object light off-axis hologram (I_(OR)) and anreference light off-axis hologram (I_(LR)), using an image sensor; and

an image reconstruction unit for deriving data of surface shape byreconstructing an image of the surface to be measured from the dataacquired by the data acquisition unit, wherein

the data acquisition unit comprises:

an optical system which is configured to make both an illumination lightcondensing point (P_(Q)) being a condensing point of the spherical waveillumination light (Q) and a reference light condensing point (P_(L))being a condensing point of the inline spherical wave reference light(L) be arranged in a mirror image of each other with respect to avirtual plane (VP) being virtually set so as to contact the surface tobe measured, and configured to make the inline spherical wave referencelight (L) obliquely pass through the virtual plane (VP) and enter theimage sensor, and

the image reconstruction unit comprises:

an object light hologram generation unit for generating an object lighthologram (g) representing the light wave of the object light (O) by acalculation process using the data of the two kinds of off-axisholograms (I_(OR), I_(LR)), position information of the reference lightcondensing point (P_(L)), and the fact that the light emitted from thereference light condensing point (P_(L)) is a spherical wave;

a reconstructed object light hologram generation unit for generating areconstructed object light hologram (h^(V)) on the virtual plane (VP) byperforming a light wave propagation calculation and a rotationaltransformation on the object light hologram (g);

a reference point detection unit for detecting, by performing a lightwave propagation calculation on the object light hologram (g), aposition at which the object light (O) is condensing, and for settingthe position as a reference point (S1), to be used for shapemeasurement, having more precise information than the positioninformation of the reference light condensing point (P_(L));

an analytical light hologram generation unit for analytically generatinga spherical wave light hologram (s^(V)) that is a hologram on thevirtual plane (VP), of a spherical wave light emitted from the referencepoint (S1); and

a shape measuring unit for generating a measurement hologram (J^(V)_(OS)=h^(V)/s^(V)) by dividing the reconstructed object light hologram(h^(V)) by the spherical wave light hologram (s^(V)), and for obtaininga height distribution of the surface to be measured of the object usinga phase distribution of the measurement hologram (J^(V) _(OS)).

Moreover, the surface shape measuring method using holography of thepresent invention, comprises the steps of:

arranging a reference light condensing point (P_(L)) being a condensingpoint of an inline spherical wave reference light (L) on an optical axisof an image sensor, arranging an illumination light condensing point(P_(Q)) being a condensing point of a spherical wave illumination light(Q) off the optical axis, and setting a virtual plane (VP) being a planethat bisects a line segment connecting the reference light condensingpoint (P_(L)) and the illumination light condensing point (P_(Q))vertically;

arranging an object so that a surface to be measured is in contact withthe virtual plane (VP), and acquiring data of an object light (O) beinga reflected light of the spherical wave illumination light (Q) reflectedfrom the surface to be measured as an object light off-axis hologram(I_(OR)) using the image sensor;

acquiring, in a state where the object is not arranged, data of theinline spherical wave reference light (L) passing through the virtualplane (VP) and being incident on the image sensor as a reference lightoff-axis hologram (I_(LR)) using the image sensor;

generating a complex amplitude inline hologram (J_(OL)) containinginformation on both the object light (O) and the inline spherical wavereference light (L) from the data of the two kinds of off-axis holograms(I_(OR), I_(LR));

generating an inline reference light hologram (j_(L)) representing alight wave of the inline spherical wave reference light (L) on ahologram plane being a light-receiving surface of the image sensor byperforming a calculation process using the fact that the inlinespherical wave reference light (L) is a spherical wave light;

generating an object light hologram (g) representing a light wave of theobject light (O) using the complex amplitude inline hologram (J_(OL))and the inline reference light hologram (j_(L));

generating a reconstructed object light hologram (h^(V)) on the virtualplane (VP) by performing a light wave propagation calculation and arotational transformation on the object light hologram (g);

detecting, by performing a light wave propagation calculation on theobject light hologram (g), a position at which the object light (O) iscondensing, and setting the position as a reference point (S1), to beused for shape measurement, having more precise information than theposition information of the reference light condensing point (P_(L));

generating a spherical wave light hologram (s^(V)) being a hologram onthe virtual plane (VP) of a spherical wave light emitted from thereference point (S1); and

generating a measurement hologram (J^(V) _(OS)=h^(V)/s^(V)) by dividingthe reconstructed object light hologram (h^(V)) by the spherical wavelight hologram (s^(V)), and obtaining a height distribution of thesurface to be measured of the object using a phase distribution of themeasurement hologram (J^(V) _(OS)).

According to the surface shape measuring device and the surface shapemeasuring method of the present invention, since the phase data of thereflected light of the spherical wave illumination light from thesurface to be measured is acquired and the phase data is compared withthe phase distribution in a plane cut surface of a spherical waveobtained analytically to perform the shape measurement, highly accuratesurface shape measurement can be realized without requiring a physicalreference plane such as a glass substrate.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowchart showing the surface shape measuring methodaccording to the 1st embodiment of the present invention.

FIG. 2 is a conceptual diagram for explaining the measuring method.

FIG. 3 is a flowchart showing a highly accurate method for determiningthe virtual plane in the measuring method.

FIG. 4 is a side view showing how the object light off-axis hologram isacquired by the surface shape measuring device according to the 2ndembodiment.

FIG. 5 is a side view showing how the reference light off-axis hologramis acquired by the device.

FIG. 6 is a side view showing a state in which the object light off-axishologram is acquired by the surface shape measuring device according tothe 3rd embodiment.

FIG. 7 is a side view showing how the object light off-axis hologram isacquired by the surface shape measuring device according to the 4thembodiment.

FIG. 8 is a side view around the image sensors of the surface shapemeasuring device according to the 5th embodiment.

FIG. 9 is a block configuration diagram of the surface shape measuringdevice according to the 6th embodiment.

FIG. 10 is an image showing a phase distribution of the complexamplitude hologram on a surface of a plane mirror sample, which isobtained using the surface shape measuring device according to thepresent invention (example 1).

FIG. 11 is an image showing a surface height distribution obtained usingthe phase distribution of FIG. 10.

FIG. 12A is a diagram of a height distribution on a straight line in thex direction in FIG. 11, and FIG. 12B is a diagram of a heightdistribution on a straight line in they direction in FIG. 11.

FIG. 13 is an image showing a surface height distribution obtained foranother flat mirror sample (example 2).

FIG. 14A is a diagram of a height distribution on a straight line in thex direction in FIG. 13, and FIG. 14B is a diagram of a heightdistribution on a straight line in they direction in FIG. 13.

FIG. 15 is an image showing a surface height distribution obtained foranother plane mirror sample (example 3).

FIG. 16A is a diagram of a height distribution on a straight line in thex direction in FIG. 15, and FIG. 16B is a diagram of a heightdistribution on a straight line in they direction in FIG. 15.

FIG. 17 is an image showing a surface height distribution obtained for anegative pattern USAF test target (example 4).

FIG. 18A is a diagram of a height distribution on a straight line in thex direction in FIG. 17, and FIG. 18B is a diagram of a heightdistribution on a straight line in they direction in FIG. 17.

FIG. 19 is an image showing a height distribution of a liquid crystaldisplay filter measured using the surface shape measuring deviceaccording to the present invention (example 5).

FIG. 20 is an enlarged image of the part within the square in FIG. 19.

FIG. 21 is a height distribution diagram showing a measurement resultalong the measurement line (i) in the image of FIG. 20.

FIG. 22 is a height distribution diagram showing a measurement resultalong the measurement line (ii) in the image of FIG. 20.

FIG. 23 is a diagram of a spacer height measurement value distributionobtained for the measurement target in FIG. 19.

MODE FOR CARRYING OUT THE INVENTION

Hereinafter, the surface shape measuring device and the surface shapemeasuring method according to embodiments of the present invention aredescribed below with reference to the drawings.

1st Embodiment: Surface Shape Measuring Method

The surface shape measuring method according to the 1st embodiment isdescribed with reference to FIG. 1 to FIG. 4. As shown in FIG. 1 andFIG. 2, the present surface shape measuring method is a method formeasuring the shape of the surface to be measured of the object 4 byusing holography, and comprises processes from the optical systemarranging step (#1) to the surface shape measuring step (#8).

In the optical system arranging step (#1), the illumination lightcondensing point P_(Q) being a condensing point of the spherical waveillumination light Q and the reference light condensing point P_(L)being a condensing point of the inline spherical wave reference light Lare arranged so as to be mirror images of each other with respect to thevirtual plane VP being set virtually. Further, the image sensor 5 isarranged on a straight line that obliquely passes through the virtualplane VP from the reference light condensing point P_(L), and the basepoint P_(O) indicating the position of the object 4 is set at theintersection position of the straight line and the virtual plane VP.Under these configurations, holograms of the spherical wave lights Q andL may be acquired by the image sensor 5 using the off-axis referencelight R, reconstructed and confirmed in a computer, and the object 4 isarranged later. After that, the position and posture of the sample stage7 and the entire optical system are adjusted. The spherical wave lightsQ, L and the off-axis reference light R are mutually coherent laserlights emitted from one light source.

The position of each the condensing points P_(Q), P_(L), that is, thelight source of each spherical wave light Q, L is set by a pinholeposition of a pinhole plate, for example. Further, the reference planesubstrate 70 having a reference plane is arranged so that the referenceplane is at the position of the virtual plane VP, and a hologram of areflected light of the spherical wave illumination light Q is acquired.The degree of accuracy required for such confirmation, adjustment, andsetting is about several tens of micrometers that can be adjusted bymechanical operation with a screw or the like. The process of increasingthe measurement precision to the order of nm (nanometer) is performed,without using a piezoelectric element or the like, by usingpost-processing in the computer at the time of image reconstruction.

In the object light hologram acquiring step (#2), the object 4 isarranged at the position of the base point P_(O) so that the surface tobe measured is in contact with the virtual plane VP. The arrangement ofthe object 4 is performed by fixing it on the sample stage 7 adjusted inadvance. The surface to be measured of the object 4 is obliquelyilluminated by the spherical wave illumination light Q, and the data, ofthe reflected light which is emitted from the object 4 as the objectlight O and incident on the image sensor 5, is acquired using theoff-axis reference light R as an object light off-axis hologram I_(OR).

In the reference light hologram acquiring step (#3), the data of theinline spherical wave reference light L, which obliquely passes throughthe virtual plane VP and is incident on the image sensor 5 in a state inwhich neither the reference plane substrate 70 nor the object 4 isarranged, is acquired using the off-axis reference light R as areference light off-axis hologram I_(LR). Data of those two types ofoff-axis holograms I_(OR), I_(LR) are not acquired at the same time.Therefore, the irradiation condition and the like of the off-axisreference light R need to be kept the same when acquiring each data.

In the object light hologram generating step (#4), the object lighthologram g representing the light wave of the object light O on thehologram plane 50 at the light receiving surface (z=0) is generated bydata processing in the computer, using the object light off-axishologram I_(OR), the reference light off-axis hologram I_(LR), and thefact that the inline spherical wave reference light L are a sphericalwave light.

In the object light measurement hologram generating step (#5), theobject light hologram g is converted into a hologram at the position ofthe base point P_(O) by a light wave propagation calculation.Transforming a hologram to a hologram at another position by the lightwave propagation calculation is called light propagation transformation.The position transformed hologram is rotationally transformed accordingto the virtual plane tilt angle α_(O) that is the tilt angle of thevirtual plane VP with respect to the hologram plane 50, and thereconstructed object light hologram h^(V) for measurement on the virtualplane VP is generated.

In the reference point detecting step (#6), the position where theobject light O is condensed is detected by performing the light wavepropagation calculation on the object light hologram g, and the detectedposition is set as the reference point S1 for shape measurement. Theposition information of the reference point S1 is more preciseinformation than the position information of the reference lightcondensing point P_(L). By using the position information of thereference point S1, it is possible to measure the surface to be measuredwith high accuracy.

In the spherical wave light hologram generating step (#7), a hologram ofa spherical wave light emitted from the reference point S1 for shapemeasurement is analytically generated as the spherical wave lighthologram s^(V) on the virtual plane VP. The spherical wave lighthologram s^(V) realizes a reference plane, corresponding to the aconventional physical reference substrate that serves as a referenceplane in the Fizeau interferometer, in a computer.

In the surface shape measuring step (#8), the reconstructed object lighthologram h^(V) is divided by the spherical wave light hologram s^(V) togenerate the measurement hologram J^(V) _(OS), which is a complexamplitude inline hologram relevant to the object light O and thespherical wave light hologram s^(V), for the measurement. From the phasedistribution of the measurement hologram J^(V) _(OS), the heightdistribution on the surface to be measured of the object 4, that is, thesurface shape of the object 4 is obtained.

(Details of Virtual Plane Setting)

The initial setting of the sample stage 7 and the optical system shownin FIG. 2 is performed as follows, for example. The setting of theposition and posture of the sample stage 7 has the same meaning as thesetting of the position and posture of the virtual plane VP. Thereference light condensing point P_(L) being the condensing point of theinline spherical wave reference light L is arranged on the optical axisof the image sensor 5, and the illumination light condensing point P_(Q)being the condensing point of the spherical wave illumination light Q isarranged at a position off the optical axis. The arrangements andsettings of the light sources (P_(Q), P_(L)) and the image sensor 5 arefixed thereafter.

The virtual plane VP is a plane that vertically bisects the line segmentconnecting the reference light condensing point P_(L) and theillumination light condensing point P_(Q). The base point P_(O)indicating the position of the object 4 is set at the intersection ofthe virtual plane VP and the optical axis. The sample stage 7 isarranged at the position of the base point P_(O) in an adjusted state.The sample stage 7 is adjusted so that the surface to be measured of theobject 4 contacts the virtual plane VP when the object 4 is fixed on thesample stage 7. The adjustment of the sample stage 7 is performed asfollows.

The reference plane substrate 70 having the reference plane is fixed onthe sample stage 7 and illuminated with the spherical wave illuminationlight Q, and data of the reflected light from the reference plane isacquired as the object light off-axis hologram I_(OR) using the off-axisreference light R. Data of the inline spherical wave reference light L,passing through the virtual plane VP and enters the image sensor 5 in astate where the reference plane substrate 70 is not arranged, isacquired as the reference light off-axis hologram I_(LR) using theoff-axis reference light R. The sample stage 7 is adjusted by changingthe position and tilt, that is, the posture of the sample stage 7, sothat the changes in the phase distribution of the complex amplitudeinline hologram J_(OL) obtained by dividing the real image component ofthe object light off-axis hologram I_(OR) by the real image component ofthe reference light off-axis hologram I_(LR) is reduced.

Explanation is made more specifically. First, without the object 4, thecondensing points of the inline spherical wave reference light L and thespherical wave illumination light Q are arranged, and the interferencefringes I_(LR) generated by the inline spherical wave reference light Land the off-axis reference light R are recorded. Next, the referenceplane substrate 70 having a reference plane of high flatness such as anoptical flat is fixed on the sample stage 7 as the object 4 andilluminated with the spherical wave illumination light Q. And then, thedistance z_(O) and the tilt angle α_(O) of the sample stage 7 areadjusted mechanically, so that the symmetry point of the illuminationlight condensing point P_(Q) with respect to the reference plane of thereference plane substrate 70 approaches the reference light condensingpoint P_(L), in other words, the reference plane of the reference planesubstrate 70 moves to the reference light condensing point P_(L), afterthat, the interference fringes I_(OR) generated by the object light Obeing a light reflected from the reference plane and the off-axisreference light R are recorded in one shot.

By performing spatial frequency filtering to extract the complexamplitude off-axis holograms J_(OR) and J_(LR) representing the realimage components, respectively, from the interference fringes I_(OR) andI_(LR), and by dividing J_(OR) by J^(LR), the complex amplitude inlinehologram J_(OL) is obtained. The phase (θ_(O)-θ_(L)) of the complexamplitude inline hologram J_(OL) represents the phase difference betweenthe inline spherical wave reference light L and the object light O(which is regarded as a spherical wave) on the hologram plane 50. Whenthe symmetry point of the illumination light condensing point P_(Q)approaches the reference light condensing point P_(L), the phasecomponent exp[i(θ_(O)−θ_(L))] of J_(OL) approaches a constant valuedistribution on the hologram plane 50. Further, when the symmetry pointof the point P_(Q) moves away from the point P_(L), the phase componentexp[i(θ_(O)−θ_(L))] becomes a changing value distribution.

When the separation distance between the symmetry point of the pointP_(Q) and the reference light condensing point P_(L) becomes theresolution δ=λ/(2NA) or more in the direction perpendicular to the zaxis, or becomes the depth of focus DOF=λ/(2NA²) or more in the z axisdirection, the distribution of the phase component exp[i(θ_(O)−θ_(L))]changes oscillatory on its hologram plane. Here, NA is the numericalaperture of the recorded hologram.

By adjusting the distance z_(O) and the tilt angle α_(O) so that thechanges in the phase component exp[i(θ_(O)−θ_(L))] of the complexamplitude inline hologram J_(OL) is sufficiently small, a plane incontact with the reference plane of the reference plane substrate 70 isdetermined as the virtual plane VP, and the adjustment of the samplestage 7 is completed. The reference light L and the illumination light Qbecame symmetrical with respect to the determined virtual plane VPsandwiched therebetween, and the two-dimensional distribution of thephase difference (θ_(O)−θ_(L)) between the illumination light Q and thereference light L on the virtual plane VP becomes almost a constantvalue of small change.

By the way, when the unevenness height t of the surface shape to bemeasured with accuracy Δt, the mechanical adjustments, at the time ofdetermining the virtual plane VP, are required to be performed so thatthe phase change Δ(θ₀−θ_(L)) becomes smaller than 4πΔt/λ, namely,Δ(θ₀−θ_(L))<4πΔt/λ. This kind of adjustment is difficult to performmechanically only with screws without using a piezoelectric driveelement such as PZT, and the measurement accuracy Δt on the nm ordercannot be expected, however, improvements of the measurement accuracy Δtare possible by performing post-processing in the computer at the timeof image reconstruction.

(Hologram Data and its Processing)

Explanation of hologram data and its processing based on mathematicalexpressions is made. In the hologram, the off-axis reference light R,the inline spherical wave reference light L, the object light O, etc areinvolved. Here, the origin of the xyz right-handed orthogonal coordinatesystem is set at the center of the hologram plane 50 (light receivingsurface of the image sensor 5) (the coordinate system regarding thevirtual plane VP is x′y′z′, see FIG. 2). The direction from the hologramplane 50 toward the light source of the object light O is the positivedirection of the z axis. By using the position coordinates (x, y), theobject light O(x, y, t), the off-axis reference light R(x, y, t), andthe inline spherical wave reference light L(x, y, t) are expressed bythe following general equations (1), (2), and (3), respectively. Thoselights having angular frequency ω are coherent with each other.Coefficients, arguments, subscripts, etc. in each equation areinterpreted in a general expression and meaning. In each of thefollowing equations, the position coordinates (x, y, z), the spatialfrequency (u, v, w), etc. are omitted as appropriate.

O(x,y,t)=O ₀(x,y)exp[i(ϕ_(O)(x,y)−ωt)]  (1)

R(x,y,t)=R ₀(x,y)exp[(ϕ_(R)(x,y)−ωt)]  (2)

L(x,y,t)=L ₀(x,y)exp[i(ϕ_(L)(x,y)−ωt)]  (3)

The light intensity I_(OR)(x, y) of a light composed of L(x, y, t) andR(x, y, t), and the light intensity I_(LR) (x, y) of a light composed ofO(x, y, t) and R(x, y, t) are expressed by following equations (4) and(5), respectively. Those light intensities I_(OR) and I_(LR) areacquired as hologram data by the image sensor 5.

I _(OR)(x,y)=O ₀ ² +R ₀ ² +O ₀ R ₀ exp[i(ϕ_(O)−ϕ_(R))]+O ₀ R ₀exp[−i(ϕ_(O)−ϕ_(R))]  (4)

I _(LR)(x,y)=L ₀ ² +R ₀ ² +L ₀ R ₀ exp[i(ϕ_(L)−ϕ_(R))]+O ₀ R ₀exp[−i(ϕ_(L)−ϕ_(R))]  (5)

In the above equations (4) and (5), the 1st term on the right side isthe light intensity component of the object light O or the inlinespherical wave reference light L, and the 2nd term is the lightintensity component of the off-axis reference light R. The 3rd term andthe 4th term of each equation are a direct image component and aconjugate image component, which are created as modulation results ofthe object light O or the inline spherical wave reference light L madeby the off-axis reference light R, respectively.

The direct image component of the 3rd term includes information of theobject light O or the reference light L necessary for the present dataprocessing method, that is, O₀exp(iφ_(O)) or L₀exp(iφ_(L)) of the aboveequations (1) and (3). In the direct image component of the 3rd term,the phase portions [iφ_(O)] and [iφ_(L)] of the object light O or thereference light L is equal to the phase portion [iφ_(O)] or [iφ_(L)] inabove equations (1) and (3) defining those lights. On the other hand, inthe 4th term, the phase portions [−iφ_(O)] or [−iφ_(L)] of the objectlight O or the reference light L is a complex conjugate of the phaseportion [iφ_(O)] or [iφ_(L)] in above equation (1) or (3) defining thoselight, and accordingly, the 4th term is called a conjugate imagecomponent.

By using the off-axis reference light R and its off-axis effect, such ahologram can be acquired in which the direct image component (the 3rdterm) is separated from the light intensity components (the 1st and 2ndterms) and the conjugate image component (the 4th term) when thehologram is expressed in a spatial frequency space. Therefore, byapplying spatial frequency filtering, only the 3rd terms of aboveequations (4) and (5) are extracted, and the object light complexamplitude hologram J_(OR) in which the object light O is recorded andthe complex amplitude hologram J_(LR) in which the inline spherical wavereference light L is recorded are derived, respectively, as shown in thefollowing equations (6) and (7). Those complex amplitude holograms areholograms still containing the components of off-axis reference light R.

J _(OR)(x,y)=O ₀(x,y)R ₀(x,y)exp[i(ϕ_(O)(x,y)−ϕ_(R)(x,y))]  (6)

J _(LR)(x,y)=L ₀(x,y)R ₀(x,y)exp[i(ϕ_(L)(x,y)−ϕ_(R)(x,y))]  (7)

The spatial frequency filtering is performed by Fourier transformingabove equations (4) and (5) into equations expressed in the spatialfrequency space, filtering using bandpass filter, and theninverse-Fourier transforming. For reference, if the pixels in the imagesensor are two-dimensionally arranged with a pixel pitch d, the highestspatial frequency fs of the hologram, recordable by using such a imagesensor, becomes a spatial frequency fs=1/d.

By dividing above equation (6) by equation (7), the amplitude R₀ and thephase φ_(R) of the off-axis reference light R can be removed from theequation (6). This processing is processing for performing phasesubtraction, that is, processing for frequency conversion, and isprocessing for heterodyne modulation. As a result, the complex amplitudeinline hologram J_(OL) of the object light O with respect to the inlinespherical wave reference light L is obtained as shown in the followingequation (8).

J _(OL)(x,y)=(O ₀(x,y)/L ₀(x,y))exp[i(ϕ_(O)(x,y)−ϕ_(L)(x,y))]  (8)

The inline spherical wave reference light L is a reference light foracquiring and storing the data of the reference light R as the referencelight hologram I_(LR) which is an off-axis hologram, and also serves asa standard light in digital processing of hologram data. The inlinespherical wave reference light L is used to generate the complexamplitude inline hologram J_(OL) that is a hologram not including thedata of the reference light R. If the off-axis reference light R ismaintained under the same conditions while a plurality of object lightholograms I^(j) _(OR) are acquired, it is enough to acquire onereference light hologram I_(LR) and to generate one complex amplitudehologram J_(LR).

(Component of Inline Spherical Wave Reference Light L and MultiplicationFactor)

Next, by multiplying both sides of equation (8) by a multiplicationfactor L₀(x, y)exp[iφ_(L)(x, y)], an amplitude modulation by theamplitude factor L₀(x, y) and a heterodyne modulation by the phasefactor exp[iφ_(L)(x, y)] is performed, and the object light hologramg(x, y) representing the light wave of the object light O on the surfaceof the image sensor 5 (hologram plane, xy plane, or plane z=0) can begenerated, as shown in the following equation (9). The process forgenerating the object light hologram g(x, y) is a process forreconstructing the object light O. The light intensity distribution ofthe object light O on the hologram plane 50 can be viewed as an image bydisplaying the square of the absolute value |g(x, y)|² of the objectlight hologram g(x, y).

g(x,y)=O ₀(x,y)exp[iϕ ₀(x,y)]  (9)

This multiplication process is a process for removing the component ofthe inline spherical wave reference light L from above equation (8), andthe hologram g only containing the light wave O₀(x, y)exp[iφ_(O)(x, y)]of the object light O is generated. The term “hologram” is used in thesense that it contains all the data necessary to reconstruct the lightwave, and will be used interchangeably below. The amplitude L₀(x, y) ofthe inline spherical wave reference light L may be left if it changesgently and can be ignored.

The multiplication factor L₀(x, y)exp[iφ_(L)(x, y)] is a hologramrepresenting a light wave reaching the image sensor 5, namely, thehologram plane 50 after being emitted from the condensing point P_(L) ofthe inline spherical wave reference light L as a spherical wave andpropagating in the air, and thus this hologram is referred to as aninline reference light hologram j_(L). The inline reference lighthologram j_(L) reaches the hologram plane 50 as a spherical wave if itpropagates only in the air to the hologram plane 50. Therefore, themultiplication factor can be analytically obtained using the positioninformation of the condensing point P_(L).

Note that, as in the optical system in FIG. 4 described later, when theinline spherical wave reference light L passes through the beam coupler3 and the like, the wave front at the hologram plane 50 is a wave frontdeformed from a spherical wave. In that case, the hologram j_(L) can notbe calculated analytically, but can be derived by light propagationcalculation using plane wave expansion if the distance ρ from thecondensing point P_(L) of the inline spherical wave reference light L tothe hologram plane 50 and the thickness dimension A of the beam coupler3 are given (described later).

(Measurement of Distances ρ and z_(O), and Tilt Angle α_(O))

In order to measure the surface shape, it is necessary to reconstructthe reflected light at the the surface to be measured, that is, at aposition parallel to the virtual plane. Therefore, in order toreconstruct the reflected light using the complex amplitude inlinehologram, following values are required: the distance z_(O) from theimage sensor 5 or the hologram plane 50 to the surface to be measured orthe virtual plane VP, the tilt angle α_(O) of the virtual plane VP withrespect to the hologram plane 50, and the distance ρ from the hologramplane 50 to the reference light condensing point P_(L) being thecondensing point of the inline spherical wave reference light L. Thosevalues can be measured by any other measuring means, but can be obtainedusing holography with high accuracy by acquiring and reconstructing atarget image.

In the optical system shown in FIG. 2, a flat target, composed of atransparent flat glass substrate having a pattern whose dimensions areaccurately known, is fixed on the adjusted sample stage 4 so that thepattern contacts the virtual plane VP. Next, the flat target isilluminated with the inline spherical wave reference light L, and theinterference fringes I_(OR) formed by the object light O, which is theinline spherical wave reference light L transmitted through the targetand the off-axis reference light R, is recorded. From the recordedinterference fringes I_(OR) and I_(LR), the object light g on thehologram plane 50 is obtained, and then plane wave expansion and lightpropagation calculation are performed on the object light g and alsorotational transformation is performed to reconstruct a focused image onthe target surface as described below.

(Plane Wave Expansion and Light Propagation Calculation)

A plane wave is an exact solution of the Helmholtz equation forelectromagnetic waves. The light wave of the object light O can beexpanded with the plane waves which are the exact solution. The planewave expansion is executed by Fourier transforming the object lighthologram g(x, y) of above equation (9). That is, the Fourier transformis the plane wave expansion. As a result of the plane wave expansion, aspatial frequency spectrum G(u, v) of the object light O is obtained asshown in the following equation (10). The spatial frequency spectrumG(u, v) is the complex amplitude of the plane wave having the wavenumber vector (u, v) and is also referred to as the complex amplitudeG(u, v). At the position translated by the distance z_(O) from thehologram plane 50, a spatial frequency spectrum H(u, v) of the objectlight O is given by the following equation (11), and an object lighth(x, y, z_(O)) is obtained by the following equation (12).

G(u,v)=∫∫g(x,y)exp[−i2π(ux+vy)]dxdy  (10)

H(u,v)=G(u,v)exp[i2w(u,v)z _(O)]  (11)

h(u,v,z _(O))=∫∫H(u,v)exp[i2π(ux+vy)]dudv  (12)

w(u,v)=√{square root over ((1/λ)² −u ² −v ²)}

(Rotational Transformation)

A spatial frequency spectrum H^(V)(u′, v′) after the rotationaltransformation by the tilt angle α_(O) is given by the followingequation (13), and the Jacobian J(u′, v′) of the rotationaltransformation is given by the following equation (14). Therefore, areconstructed object light h^(V)(x′, y′, z_(O)) after the rotationaltransformation is given by the following equation (15).

H ^(V)(u′,v′)=H(u′ cos α₀ −w′ sin α_(O) ,v′)J(u′,v′)  (13)

J(u′,v′)=cos α₀−(u′/w′)sin α_(O)  (14)

h ^(V)(x′,y′,z _(O))=∫∫H ^(V)(u′,v′)exp[i2π(u′x′+v′y′)]du′dv′  (15)

At the base point P_(O), a reconstructed image parallel to the hologramplane 50 before the rotational transformation is obtained by |h|², and areconstructed image parallel to the virtual plane VP after therotational transformation is obtained by |h^(V)|². The reconstructedobject light h^(V) includes the distance z_(O) and the distance ρ asparameters. At least around the base point P_(O), the distance z_(O) isobtained as a z coordinate value of a reconstruction surface when anin-focus reconstructed image is obtained, and the distance ρ is obtainedas a parameter value when the size of the in-focus reconstructed imagematches the actual size of the target. Further, the reconstructed objectlight h^(V) includes the tilt angle α_(O) in addition to the distancez_(O) and the distance ρ as parameters. When the in-focus reconstructedimage is obtained on the entire surface, the tilt angle α_(O) isobtained as a value of the rotational transformation angle.

(High-Precision Determination of Reference Point and Virtual Plane forShape Measurement Using Correlation Function)

Next, highly accurate determination of the virtual plane VP isexplained. Here, the distance and the measurement accuracy is described.The inline spherical wave reference light L is a light used only forreconstructing holograms, and the distance ρ to the reference lightcondensing point P_(L) is a distance measured in mm order. For the shapemeasurement, the reference light condensing point P_(L) is not used, buta reference point and a reference point light source set there are used,wherein the reference point is searched for and newly set in thevicinity of the reference light condensing point P_(L). This referencepoint is given as a true mirror image point of the illumination lightcondensing point P_(Q). This reference point is searched and set bypost-processing on the computer using the correlation functioncalculation so that it substantially comes to the position of theoriginal mirror image point of the illumination light condensing pointP_(Q).

In order to secure the required measurement accuracy, it is necessary tomake the difference ΔD_(QS)=|D_(Q)−D_(S)| between the distances D_(Q)and D_(Q) smaller than the required measurement accuracy, wherein D_(Q)is the distance between the base point P_(O) and the illumination lightcondensing point P_(Q) and D_(S) is the distance between the base pointP_(O) and the reference point light source for shape measurement. Thisis realized by post-processing on a computer. This post-processing is aprocessing for increasing the number of significant digits.

In determining the virtual plane VP using the reference plane substratedescribed above, the distance z_(O) of the reference plane and the tiltangle α_(O) are mechanically adjusted. Here, a method for determiningthe reference point light source for shape measurement with highaccuracy by calculation using a correlation function of a point lightsource and the reconstructed object light is described. The determiningof the reference point light source with high precision means thematching of the reference point light source for shape measurement witha symmetry point P1 of the illumination light condensing point P_(Q). Inorder to do this, the position of the point P1, which is considered tobe in the immediate vicinity of the reference light condensing pointP_(L), is obtained by numerical calculation using a correlation functionof lights.

As shown in the flowchart of FIG. 3, the object light hologram g for theobject light O that is the reflected light of the illumination light Qis propagated to the position z=ρ of the reference light condensingpoint P_(L) by the light propagation calculation, and the generatedhologram is set as an evaluation hologram h0=h(x, y, ρ) (#61). Next, bythe correlation function calculation between a probe function fprepresenting a point light source and the evaluation hologram h0,position coordinates (x1, y1, ρ) of a condensing point, at which theobject light O (reflected light of the illumination light Q) condenses,are detected in the plane of the evaluation hologram h0 and set as atemporary condensing point P1(x1, y1, ρ) (#62).

By fixing the position (x1, y1) of the temporary condensing point P1 ina plane orthogonal to the optical axis, by tentatively propagating theevaluation hologram h0=h(x, y, ρ) in the optical axis direction by lightpropagation calculation, and by performing the correlation functioncalculation, a condensing point of the object light O in the opticalaxis direction is detected, and thus the position coordinates (x1, y1,z1), z1=ρ+Δρ of the condensing point P1 are detected (#63). The detectedcondensing point P1(x1, y1, z1) is set as the reference point S1 forshape measurement, and a point light source of reference light is setthere (#64).

The above processes are specifically explained using mathematicalexpressions. The evaluation hologram h0=h(x, y, ρ) is given by thefollowing equation (16) (#61). The probe function fρ is a virtual pointlight source fp=δ(x−x1)δ(y−y1) placed at coordinates (x1, y1, ρ). Thecorrelation function C is given by the following equation (17).

h(x,y,ρ)=∫∫G(u,v)exp[i2πw(u,v)ρ]·exp[i2π(ux+vy)]dudv  (16)

c(x ₁ ,y ₁ ,φ=∫∫h(u,v,ρ)δ(x−x ₁)δ(y−y₁)dxdy=∫∫G(u,v)exp[i2πw(u,v)ρ]·exp[i2π(ux ₁ +vy ₁)]dudv  (17)

The correlation function C(x1, y1, ρ) includes the coordinates (x1, y1)of the virtual point light source in the plane as a parameter. Thecoordinates (x1, y1) are obtained by numerical calculation as parametervalues that maximize the absolute value |C(x1, y1, ρ)| of thecorrelation function (#62).

Next, in the equation (17), the values of (x1, y1) are fixed, ρ isreplaced with a parameter z1, and the value of z1 is obtained as a z1value which gives the maximum of the absolute value |C(x1, y1, z1)|. Asa result, the position coordinates (x1, y1, z1) of the mirror imagepoint P1 are detected (#63). By the calculation using such a correlationfunction, the coordinates (x1, y1) can be obtained with much higherprecision than the resolution δ=λ/(2NA), and the value of z1 can beobtained with much higher precision than the depth of focus DOF=(2NA²).By the above calculation, the coordinates (x1, y1, z1) of the point P1which is set as the reference point S1 can be accurately determined bynumerical calculation at the position of the reference light condensingpoint P_(L) or in the vicinity thereof (#64).

As described above, the reference point S1 for shape measurement isnewly arranged at the point P1 by using the correlation function C, anda light generated by a point light source arranged at this referencepoint S1 (hereinafter, the light generated by the reference point lightsource S1) is a spherical wave light and referred to as an inlinespherical wave reference light L1. The phase of the reference light L1generated by the reference point light source S1 can be accuratelycalculated using the analytical solution of the spherical wave. On thevirtual plane VP, the phase of the illumination light Q and the phase ofthe reference light L1 match each other over the entire virtual planeVP.

When the reconstructed object light hologram h^(V)(x′, y′) is divided bythe spherical wave light hologram s^(V)(x′, y′), the measurementhologram J^(V) _(OS)(x′, y′) for measuring the surface to be measured isobtained. The height distribution t(x′, y′) of the surface to bemeasured is obtained from the optical path difference between theillumination light Q reflected by the surface to be measured and theillumination light Q reflected by the virtual plane VP. The phase of theinline spherical wave reference light L1 having the reference point S1as the light source matches the phase of the illumination light Q on thevirtual plane VP. Therefore, the height distribution t(x′, y′) isobtained by the following equation (18) using the phase (θ_(O)−θ_(L1))of the measurement hologram J^(V) _(OS). Here, the phase θ_(O) is thephase of the reconstructed object light obtained from the reconstructedobject light hologram h^(V), the phase θ_(L1) is the phase of thereference light L1 generated by the reference point light source S1, andthe angle α(x′, y′) is the incident angle of the illumination light Q atthe coordinate (x′, y′).

$\begin{matrix}{{t\left( {x^{\prime},y^{\prime}} \right)} = {{- \frac{\left( {{\theta_{O}\left( {x^{\prime},y^{\prime}} \right)} - {\theta_{L1}\left( {x^{\prime},y^{\prime}} \right)}} \right)}{4\pi}}{\lambda cos}{\alpha\left( {x^{\prime},y^{\prime}} \right)}}} & (18)\end{matrix}$

(2nd Embodiment: Surface Shape Measuring Device)

The surface shape measuring device 1 according to the 2nd embodiment isdescribed with reference to FIG. 4 and FIG. 5. The surface shapemeasuring device 1 is a device that measures the shape of the surface tobe measured of the object 4 by using holography, and comprises the dataacquisition unit 10 for acquiring the data of holograms of the surfaceto be measured of the object 4, and the image reconstruction unit 12 forreconstructing images on the surface to be measured from the hologramsacquired by the data acquisition unit 10.

The data acquisition unit 10 comprises: the image sensor 5 forconverting light intensity into electric signals and outputting them ashologram data; the sample stage 7 for fixing the object 4 so that thesurface to be measured of the object 4 contacts the virtual plane VPbeing virtually set; and the optical system 2 for propagating eachlight. The image sensor 5 is connected to the computer 11 as a controlunit and a memory.

The optical system 2 comprises two optical systems for the sphericalwave illumination light Q and for the inline spherical wave referencelight L, which are symmetrically arranged on both sides of the virtualplane VP that is virtually set, the beam coupler 3 arranged in front ofthe image sensor 5 and composed of a cube-type beam splitter, and anoptical system for the off-axis reference light R.

The spherical wave illumination light Q is a light that illuminates thesurface to be measured of the object 4 from an oblique direction andcauses the image sensor 5 to record the reflected light including thesurface shape information of the object 4, that is, the object light O.The optical path of the illumination light Q is provided with the lens21 for condensing parallel light and the pinhole plate 22 having apinhole at the condensing position. The position of the pinhole is thecondensing point of the illumination light Q, namely, the illuminationlight condensing point P_(Q), and is the position of the point lightsource of the spherical wave light.

The optical path of the inline spherical wave light L, like theillumination light Q, is provided with the lens 25 for condensingparallel light and the pinhole plate 26 having a pinhole at thecondensing position. The position of the pinhole of the pinhole plate 26is the condensing point of the inline reference light L, namely, thereference light condensing point P_(L), and is the position of the pointlight source of the spherical wave light. The inline spherical wavelight L becomes an inline light with respect to the object light O whichis the reflected light of the illumination light Q. The recording of thereference lights L and R is used for replacing the component of theoff-axis reference light R in the recorded hologram of the object lightwith the component of the inline spherical wave light L, to remove thecomponent, and to make the recording hologram inline.

The object light O and the inline spherical wave reference light L passthrough the beam coupler 3 and enter the image sensor 5 from the front.That is, the illumination light condensing point P_(Q) and the referencelight condensing point P_(L) are optically inline and exist at the sameoptical position in the direction perpendicular to the center of thelight receiving surface of the image sensor 5.

The off-axis reference light R, enters the beam coupler 3 from the sidethereof, is reflected by the internal reflecting mirror 30, and entersthe image sensor 5. The optical path is provided with the small diameterlens 23 for expansion and the large-diameter lens 24 for collimation,and the off-axis reference light R formed in a spherical wave like shapeis generated.

In the optical system 2, the illumination light condensing point P_(Q)being the condensing point of the spherical wave illumination light Qand the reference light condensing point P_(L) being the condensingpoint of the inline spherical wave reference light L are set to be amirror image arrangement mutually relative to the virtual plane VP.Further, the optical system 2 propagates each light, so that theillumination light Q illuminates the surface to be measured obliquely,the object light O being reflected light thereof enters the image sensor5, and the inline spherical wave reference light L obliquely passesthrough the virtual plane VP and is incident on the image sensor 5.

The beam coupler 3 combines the object light O or the inline sphericalwave reference light L and the off-axis reference light R and makes themincident on the image sensor. A cube-type beam splitter may be used asthe beam coupler 3.

The image reconstruction unit 12 is provided in the computer 11 togetherwith the data storage unit 6. The image reconstruction unit 12 isconfigured to include a memory and a software group for executing thesurface shape measuring method described in the 1st embodiment.

In the surface shape measurement of the surface to be measured of theobject 4, as shown in FIG. 4, the recording hologram I_(OR) of theobject light O being reflected light is acquired using the sphericalwave illumination light Q and the off-axis reference light R in thestate that the object 4 is arranged. Further, as shown in FIG. 5, therecording hologram I_(LR) of the off-axis reference light R is acquiredusing the inline reference light L in the state that the object 4 isremoved.

The acquired off-axis holograms I_(OR), I_(LR) are processed by thesurface shape measuring method described in the 1st embodiment to obtainsurface shape measurement values. By the way, since the surface shapemeasuring device 1 of the present embodiment includes the cube-type beamcoupler 3, it is necessary to perform the light propagation calculationon the light passing through the beam coupler 3 using the plane waveexpansion method in consideration of the refractive index of the beamcoupler 3. Below, the process regarding the beam coupler 3 is described.

(Calculation of Spherical Wave after Passing Through Beam Coupler)

In order to generate the object light hologram g from the complexamplitude hologram J_(OL) on the hologram plane 50, the light wave ofthe inline spherical wave reference light L having reached the hologramplane 50 through the beam coupler 3 (inline reference light hologramj_(L)) is necessary. The inline reference light hologram j_(L) is not aspherical wave because it has passed through the beam coupler 3.Therefore, by performing the light propagation calculation on a lightwave propagating from the position of the condensing point P_(L) of theinline spherical wave reference light L to the hologram plane 50 beingthe incident surface of the image sensor 5, the inline reference lighthologram j_(L), namely, the inline spherical wave reference light L onthe hologram plane 50 is generated.

The light propagation calculation is performed using the plane waveexpansion. The inline reference light hologram j_(L) is derived byperforming the plane wave expansion on the reference light L at thecondensing point P_(L), propagating each plane wave component in the airand in the beam coupler 3 to calculate each plane wave component on thehologram plane 50, and adding up the calculated plane wave components toform the inline reference light hologram j_(L). The point light sourceb₀δ(x)δ(y) of the inline spherical wave reference light L exists on thexy plane at the position z=ρ of the condensing point P_(L). An spatialfrequency spectrum B(u, v) of this point light source is a constantvalue b₀, namely, B(u, v)=b₀. Therefore, due to the propagation of theplane wave, the inline spherical wave reference light L on the hologramplane 50 at z=0, namely, the inline reference light hologram j_(L) isgiven by the following equations (19).

$\begin{matrix}{j_{L} = {{{L_{0}\left( {x,y} \right)}{\exp\left( {i{\phi_{L}\left( {x,y} \right)}} \right)}} = {b_{0}{\int{\int{\exp{\left\{ {{- i}2{\pi\left\lbrack {{{w_{n}\left( {u,v} \right)}A} + {{w\left( {u,v} \right)}\left( {\rho - A} \right)}} \right\rbrack}} \right\} \cdot {\exp\left\lbrack {i2{\pi\left( {{ux} + {vy}} \right)}} \right\rbrack}}{dudv}}}}}}} & (19)\end{matrix}$${{w\left( {u,v} \right)} = \sqrt{\left( {1/\lambda} \right)^{2} - u^{2} - v^{2}}}{{w_{n}\left( {u,v} \right)} = \sqrt{\left( {n/\lambda} \right)^{2} - u^{2} - v^{2}}}$

In the above equation, n is the refractive index of the beam coupler 3.The above equation (19) is a function of the distance ρ from the originz=0 to the condensing point P_(L) and the dimension A of the beamcoupler 3, but is independent of the distance from the origin to thebeam coupler 3. That is, the same equation is obtained regardless of theposition of the beam coupler 3. The above equation (19) is a theoreticalcalculation equation, and in actual calculation, it is necessary toperform the light propagation calculation with the number of calculationpoints satisfying the sampling theorem.

(Object Light g(x, y) on Hologram Plane)

The inline reference light hologram j_(L) of the above equation (19)obtained by the above procedure is the light wave of the inlinespherical wave reference light L that has passed through the beamcoupler 3 and reached the hologram plane 50. By multiplying the aboveequation (8) by the multiplication factor j_(L) composed of thishologram j_(L)=L₀(x, y)exp[iφ_(L)(x, y)], the object light hologram g(x,y) representing the light wave of the object light O on the surface ofthe image sensor 5 (hologram plane, xy plane, or plane z=0) is obtainedin the same manner as in the above equation (9).

(Light Propagation Calculation)

As a result of the plane wave expansion, namely, the Fouriertransformation of the object light hologram g(x, y) on the hologramplane, a spatial frequency spectrum G(u, v) for the object light O isobtained as in the following equation (20). Expressionally, it is thesame as the above equation (10). By the light propagation calculation ofthe plane waves, an object light h(x, y) on a plane parallel to thehologram plane 50 at the position z=z_(O) of the surface to be measuredof the object 4 is obtained by the following equation (21).

G(u,v)=∫∫g(x,y)exp[−2π(ux+vy)]dxdy  (20)

h(x,y)=∫∫G(u,v)exp{i2π[w _(n)(u,v)A+w(u,v)(z _(O)−A)]}·exp[i2π(ux+vy)]dudv  (21)

In the above equation (20), u and v are Fourier spatial frequencies inthe x direction and the y direction, respectively. The Fourier spatialfrequencies w and w_(n) in the z direction are obtained from thedispersion equation of the plane wave (the relational equation betweenthe wave number and the wavelength) as annotated in the above equation(19). The dispersion equation includes the refractive index n in theform (n/λ)². The above equations (20) and (21) are calculation equationsin consideration of the size A and the refractive index n of the beamcoupler 3 existing on the optical path.

The object light h(x, y) on a plane parallel to the hologram plane 50 atthe position z=z_(O) of the surface to be measured of the object 4 isobtained by the above equation (21), and thus by executing the processesof the rotational transformation of the above equations (13) to (18),the highly accurate determination of the virtual plane using thecorrelation function, and the calculation of the height distribution,the surface shape measurement can be executed and the measurement resultcan be obtained. The processes of the above equations (13) to (18) areprocesses on phenomena in the air, and it is not necessary to considerthe influence of the refractive index n of the beam coupler 3 and thelike.

3rd Embodiment

The surface shape measuring device 1 according to the 3rd embodiment isdescribed with reference to FIG. 6. The surface shape measuring device 1according to the present embodiment is the same as the surface shapemeasuring device 1 according to the 2nd embodiment, except that theoptical system 2 comprises the condenser lens 27 for condensing theobject light O and the inline spherical wave reference light L, thepupil plate 27 a arranged at the condensing position defined by thecondenser lens 27 so as to limit the amount of passing light, and theimaging lens 27 b arranged in combination with the pupil plate 27 a. Thetwo lenses provided in front of and behind the pupil plate 27 a arelenses for imaging the object light O and the inline spherical wavereference light L on the image sensor 5.

If a large-diameter hologram can be recorded, the surface shape of alarge object can be measured. As a method for recording a large diameterhologram, a method of using a number of image sensors arranged on aplane or a method using an image sensor moving on a plane can beconsidered, however, as in this embodiment, a large diameter hologramcan be recorded using one image sensor 5 by condensing a reflected lightusing a lens. The inline spherical wave reference light L or the objectlight O is projected on the light receiving surface of the image sensor5 by using the condenser lens, and the interference fringes formed bythe off-axis reference light R are recorded. The width of the spatialfrequency band of the recording hologram can be adjusted by opening andclosing the pupil of the pupil plate 27 a. When the surface to bemeasured is smooth and has high flatness, the spatial frequencybandwidth becomes narrow, and when the surface to be measured has fineirregularities, the bandwidth becomes wide.

Since the two lenses of the condenser lens 27 and the imaging lens 27 bmake an image of the light from the surface to be measured on the lightreceiving surface of the image sensor 5, the shape of the surface to bemeasured can be observed or measured without performing thereconstruction of the object light.

4TH EMBODIMENT

The surface shape measuring device 1 according to the 4th embodiment isdescribed with reference to FIG. 7. The surface shape measuring device 1of the present embodiment has the concave mirror 28, the pupil plate 28a, and the imaging lens 28 b instead of the condenser lens 27, the pupilplate 27 a, and the imaging lens 27 b in the surface shape measuringdevice 1 of the 3rd embodiment. As the concave mirror 28, for example, acondensing elliptical mirror may be used. Also in the present surfaceshape measuring device 1, the concave mirror 28 and the imaging lens 28b make an image of the object light O and the inline spherical wavereference light L on the image sensor 5.

Also in the present surface shape measuring device 1, a hologram with alarge diameter can be recorded by a small image sensor, and it becomespossible to observe and measure the shape of the surface to be measuredwithout reconstructing the object light.

5TH EMBODIMENT

The surface shape measuring device 1 and the surface shape measuringmethod according to the 5th embodiment is described with reference toFIG. 8. The device and method of this embodiment extend the range ofmeasurable heights, and lights of different wavelengths (λ_(j), j=1, 2)are used to realize the extension. The optical system 2 of the surfaceshape measuring device 1 of the present embodiment has two pairs of awavelength filter and an image sensor, wherein such a wavelength filteris inserted between the beam coupler 3 and the image sensor 5 in theoptical system 2 of the 2nd embodiment (FIG. 4) described above.

That is, one set of the wavelength filter F1 passing one wavelength λ₁and the image sensor 51 is arranged on the side opposite to the incidentsurface 31 of the beam coupler 3 for the object light O. Another set ofthe wavelength filter F2 passing another wavelength λ₂ and the imagesensor 52 is arranged on the side opposite to the incident surface ofthe beam coupler 3 for the off-axis reference light R.

(Measurement of Surface Shape Using Phase Difference Between Light Waveswith Different Wavelengths)

In the surface shape measuring method of this embodiment, followingprocessing is performed. The data of the object light O and the inlinespherical wave reference light L are acquired by the lights of differenttwo type wavelengths λ_(j), j=1, 2 as off-axis holograms I^(j) _(OR),I^(j) _(LR), j=1, 2 for wavelength λ₁, λ₂, respectively. Next, themeasurement holograms J_(j) ^(V) _(OS)=h_(j) ^(V)/s_(j) ^(V), j=1, 2 aregenerated for each wavelength λ₁, λ₂, and a heterodyne conversion forobtaining the ratio of the two generated measurement holograms J_(j)^(V) _(OS), j=1, 2 is performed. As a result of the heterodyneconversion, the modulated wave HW=J₁ ^(V) _(OS)/J₂ ^(V) _(OS) isgenerated. The height distribution of the surface to be measured of theobject is derived using the modulated wavelength λB=λ₁λ₂/(λ₂−λ₁) and themodulated phase distribution θ_(B)(x′, y′)=θ₁−θ₂ included in themodulated wave HW.

The background and effects of the above processing is explained. Forexample, in the surface shape measurement using the phase of themonochromatic laser light shown in the 2nd embodiment, it is difficultto measure the height that greatly exceeds the light wavelength λ. Inaddition, for a step difference exceeding λ/2, an ambiguity of anintegral multiple of λ/2 is involved in the measured height value. Bythe way, when a calculation process is performed on two light waveshaving different light wavelengths whose propagation directions match, awave having a long wavelength can be generated. By using the phase ofsuch a wave, the measurable height range can be greatly extended.

The spherical wave illumination lights Q having the wavelengths λ₁ andλ₂ emitted from the same point light source have the same propagationdirection of light at all points in space, and the phase components canbe expressed as exp(2πr/λ₁−θ₁) and exp(2πr/λ₂−θ₂), respectively. Whenthe spherical wave illumination light Q having the light wavelength λ₁is divided by the spherical wave illumination light Q having the lightwavelength λ2, a wave having a phase component exp(2πr/λ_(B)−θ_(B)) isgenerated. Here, λ_(B) and θ_(B) are given by the following equations(22). The wavelength λ_(B) matches the wavelength of the beat wavecreated by two illumination lights.

λ_(B)=(λ₁λ₂)/(λ₂−λ_(k)),θ_(B)=θ₁−θ₂  (22)

When the surface to be measured is illuminated with two spherical waveswith the same light source position but different wavelengths, thepropagation directions of the two reflected lights emitted from eachpoint on the measurement surface are the same. In addition, thepropagation directions of the two reflected lights, emitted from theminute surface on the measurement surface, where the interference anddiffraction of the light near the surface can be ignored, also coincide.Therefore, when the reflected light of the light wavelength λ₁ isdivided by the reflected light of the light wavelength λ₂, it ispossible to generate a light wave of the wavelength λ_(B) having alarger wavelength that functions as in the case of the illuminationlight Q. This means that the surface shape can be measured according tothe measuring method shown in the second embodiment or the like by usingthe generated wave having the wavelength λ_(B). If the phase differencebetween two waves of wavelength λ_(B) is represented by Δθ_(B)(x′, y′),in which one wave is on the surface to be measured and the other onewave is on the virtual plane VP, the height t(x′, y′) of the surface tobe measured is given by the following equation (23). This equation (23)is equivalent to the equation (18) for a single wavelength.

$\begin{matrix}{{{t\left( {x^{\prime},y^{\prime}} \right)} = {{- \frac{\Delta{\theta_{B}\left( {x^{\prime},y^{\prime}} \right)}}{4\pi}}\lambda_{B}\cos{\alpha\left( {x^{\prime},y^{\prime}} \right)}}}{{\Delta{\theta_{B}\left( {x^{\prime},y^{\prime}} \right)}} = {{\theta_{BO}\left( {x^{\prime},y^{\prime}} \right)} - {\theta_{{BL}1}\left( {x^{\prime},y^{\prime}} \right)}}}} & (23)\end{matrix}$

The above equation (23) is basically the same as the equation (18) for asingle wavelength. The surface shape measuring device 1 and the surfaceshape measuring method according to the present embodiment canarbitrarily determine whether to use both data of the holograms acquiredfor two wavelengths or one of the data, at the time of post-processing.When using the data of both wavelengths, the equation (23) may be used,and when using the data of a single wavelength, the equation (18) may beused.

Holograms with different wavelengths can be recorded in one shot byusing the optical system in FIG. 8. In this case, in addition to theoff-axis reference light R₁ for the light wavelength λ₁, the off-axisreference light R₂ for the light wavelength λ₂ is prepared. In thisoptical system, the wavelength filter F1 that transmits the light ofwavelength λ₁ and blocks the light of wavelength λ₂ and the wavelengthfilter F2 that transmits the light of wavelength λ₂ and blocks the lightof wavelength λ₁ are used in order to separate each wavelength componentof the lights.

As another optical system 2 for the measuring method of this embodiment,for example, there is the optical system of FIG. 4 including only oneimage sensor 5 without any wavelength filter, and by using such aoptical system, two types of off-axis holograms I^(j) _(OR) and I^(j)_(LR) may be acquired at different times for each wavelength.

As yet another optical system 2, in the optical system of FIG. 4, anoptical system for the off-axis reference light R may be provided foreach wavelength. In this case, by arranging the two off-axis referencelights R₁ and R₂ in an off-axis arrangement, it becomes possible torecord one-shot holograms having different wavelengths. Separation intoholograms for each wavelength can be performed by post-processing due tothe effect of the off-axis arrangement. By performing a filteringprocess in the spatial frequency domain, the complex amplitudecomponents of the optical wavelength λ₁ and λ₂ can be separated andextracted from the one-shot recorded hologram.

Note that when using two optical systems that are off-axis arranged forthe off-axis reference light R, the recordable measurement surface maybecome narrower than when using the optical system of FIG. 8. On thecontrary, in the case of the optical system of FIG. 8, the recordablemeasurement surface can be made large, but since the two holograms arerecorded by different image sensors 51 and 52, when reconstructing theobject light O, two times position adjustments are necessary for thereconstructed lights.

According to the surface shape measuring device 1 and the surface shapemeasuring method of the present embodiment, the combined wavelengthλ_(B)=(λ₁λ₂)/(λ₂−λ₁) becomes longer than any of the original wavelengthsλ₁ and λ₂, and therefore the measurable height range can be extended.The surface shape measuring device 1 and the surface shape measuringmethod using lights of different wavelengths are not limited to lightsof two wavelengths, and can be extended to device and method using aplurality of lights of three or more wavelengths. This method canperform the measurement, by post-processing the recorded hologram data,which is significantly different from the conventional method using thebeat wave. Therefore, for example, in the case of 3 wavelengths λ₁, λ₂,λ₃, by selecting 2 wavelengths by post-processing, for example, making aplurality of combinations such as difference (1/λ₁−1/λ₂) or using all 3wavelengths, for example, a plurality of combinations such as the sumand the difference (1/λ₁+1/λ₂−1/λ₃) can be created, and the measurementrange can be interpolated with each other to perform the wholemeasurement.

6th Embodiment

The surface shape measuring device 1 according to the 6th embodiment isdescribed with reference to FIG. 9. The surface shape measuring device 1of the present embodiment can be embodied by, for example, the surfaceshape measuring device 1 shown in FIG. 5 and FIG. 6, and therefore thesefigures are also referred to. The surface shape measuring device 1comprises the data acquisition unit 10 that acquires holograms of thesurface to be measured, and the image reconstruction unit 12 thatreconstructs images on the surface to be measured from the hologramsacquired by the data acquisition unit 10. The surface shape measuringdevice 1 further comprises the control unit 11 including a computer thatcontrols the data acquisition unit 10 and the image reconstruction unit12, and the memory 11 a that stores calculation programs such as FFT andcontrol data.

The data acquisition unit 10 comprises the optical system 2 thatgenerates and propagates lights, the beam coupler 3 that is a cube-typebeam splitter used as a beam coupler, the image sensor 5 that convertslight intensity into electrical signals and outputs them as hologramdata, and the data storage unit 6 that stores data acquired by the imagesensor 5. The data storage unit 6 is provided in the control unit 11together with the image reconstruction unit 12. The data acquisitionunit 10 also comprises the sample stage 7 whose position and posture canbe adjusted in relation to the arrangement of the optical system 2 andthe image sensor 5.

The image reconstruction unit 12 comprises the hologram generating units13 to 16 and 18, the reference point detecting unit 17, the shapemeasuring unit 19, and the display unit 20 in order to perform theprocesses of the respective steps shown in FIG. 1 and FIG. 3.

The complex amplitude hologram generation unit 13 removes the componentof the off-axis reference light R from the object light off-axishologram I_(OR) and the reference light off-axis hologram I_(LR) togenerate the complex-amplitude inline hologram J_(OL) for the objectlight O and the inline spherical wave reference light L.

The calculation reference light hologram generation unit 14 generatesthe inline reference light hologram j_(L) representing the light wave ofthe inline spherical wave reference light L on the hologram plane 50 atthe light receiving surface of the image sensor, based on that the lightemitted from the reference light condensing point P_(L) is a sphericalwave.

The object light hologram generation unit 15 generates the object lighthologram g representing the light wave of the object light O on thehologram plane 50 from the complex amplitude inline hologram J_(OL)using the inline reference light hologram j_(L).

The reconstructed object light hologram generation unit 16 generates thereconstructed object light hologram h^(V) for measurement on the virtualplane VP, by converting the object light hologram g into the hologram atthe position of the virtual plane VP by the light propagationcalculation, and by performing the rotational transformation on theconverted hologram by the virtual plane tilt angle α_(O) being the tiltangle of the virtual plane VP with respect to the hologram plane 50.

The reference point detection unit 17 performs the light propagationcalculation of the object light hologram g, detects the condensing pointof the object light by the correlation function calculation, and setsthe point as the reference point S1 for shape measurement.

The analytical light hologram generation unit 18 analytically generatesthe spherical wave light hologram s^(V) which is a hologram on thevirtual plane VP of the spherical wave corresponding to the inlinespherical wave reference light L emitted from the reference lightcondensing point P_(L).

The shape measuring unit 19 divides the reconstructed object lighthologram h^(V) by the spherical wave light hologram s^(V) to generatethe measurement hologram J^(V) _(OS) relating to the object light O andthe spherical wave light hologram s^(V), and calculates the heightdistribution of the surface to be measured of the object 4 from thephase distribution of the complex amplitude inline hologram J^(V) _(OS)for measurement.

The display unit 20 displays images obtained by the image sensor 5,intensity images of each hologram, phase distribution images, and thelike. The data of the object light off-axis hologram I_(OR) and thereference light off-axis hologram I_(LR) stored in the data storage unit6 are processed by the image reconstruction unit 12 and displayed on thedisplay unit 20. The display unit 20 is an FPD such as a liquid crystaldisplay device, displays data other than images too, and serves as auser interface. Except for the display unit 20, each unit of the imagereconstruction unit 12 is configured by using programs running on acomputer and software including a group of their subroutines.

Example 1

The flatness measurement of the example 1 is described with reference toFIG. 10, FIG. 11, and FIG. 12. Using a plane mirror of a float glasssubstrate having a flatness specification of 4λ to 5λ as a sample forflatness measurement, a complex amplitude inline hologram for shapemeasurement was obtained using the optical system shown in FIG. 4 andFIG. 5. A green semiconductor pumped solid-state laser (wavelength 532nm, output 50 mW) was used as a light source, and a monochrome cameralink CCD camera (number of pixels 6600×4400, pixel pitch 5.5 μm) wasused as an image sensor. Each of the spherical wave lights used for theinline spherical wave reference light and the spherical waveillumination light was generated using an objective lens with anumerical aperture NA=0.1 and a pinhole with an aperture diameter of 3μm. The pinhole was placed at a position 567 mm away from the imagesensor surface, and a surface to be measured was placed at a position13.9 mm away. The numerical aperture of the recorded hologram (pixelnumber 4096×4096) is NA=0.02.

FIG. 10 shows the phase distribution of the complex amplitude inlinehologram on the mirror surface of the plane mirror having the flatnessspecifications of 4λ to 5λ.

FIG. 11 shows the two-dimensional distribution of the surface heightsobtained by using the phase distribution of FIG. 10. The differencePV=431.7 nm between the maximum value and the minimum value of thesurface height and the standard deviation RMS=69.0 nm of the height wereobtained in the measurement area 15 mm×15 mm. In the measurement area,the PV value is smaller than A and satisfies the flatness specifications4λ to 5λ. FIG. 12A and FIG. 12B show the height distributions on thestraight lines in the x-axis and y-axis directions shown in FIG. 11,respectively. As the radius of curvature in the x-axis direction shownin FIG. 12A, about 160 m was obtained.

Example 2

The flatness measurement of the example 2 is described with reference toFIG. 13, FIG. 14A and FIG. 14B. The complex amplitude inline hologramfor shape measurement was obtained for a plane mirror having a flatnessspecification of λ/4 as a sample for flatness measurement, using thedevice used in the example 1.

FIG. 13 shows the two-dimensional distribution of the surface height ofthe plane mirror having the flatness specification λ/4. The differencePV=81.3 nm between the maximum value and the minimum value of thesurface height and the standard deviation RMS=15.3 nm of the height wereobtained. In the measurement area, the PV value is smaller than λ/4 andsatisfies the flatness specification λ/4. FIG. 14A and FIG. 14B show theheight distributions on the straight lines in the x-axis and y-axisdirections shown in FIG. 13. As the radius of curvature in the y-axisdirection shown in FIG. 14B, about 750 m was obtained. The resolution ofthe surface shape measurement is determined by the bandwidth of thespatial frequency filtering performed on the reconstructed object light.The resolution of the image in the examples 2, 3(SIC) is about 78 μm.

Example 3

The flatness measurement of the example 3 is described with reference toFIG. 15, FIG. 16A and FIG. 16B. The complex-amplitude inline hologramfor shape measurement was obtained for a precision optical flat mirrorhaving a flatness specification of λ/20 as a sample for flatnessmeasurement, using the device used in the example 1.

FIG. 15 shows the two-dimensional distribution of the surface height ofthe plane mirror having the flatness specification λ/4(SIC). Thedifference PV=19.6 nm between the maximum value and the minimum value ofthe surface height and the standard deviation RMS=2.5 nm of the heightwere obtained. In the measurement area, the PV value is smaller thanλ/20 and satisfies the flatness specification λ/20.

FIG. 16A and FIG. 16B show the height distributions on the straightlines in the x-axis and y-axis directions shown in FIG. 15,respectively.

The recorded object light contains weak multiple reflected lightsgenerated on the surface of the cube-type beam splitter (beam coupler)and on the surface of the cover glass fixed on the front of the imagesensor. By slightly inclining the surfaces of the beam splitter and thecover glass from the image sensor surface, the propagation direction ofthese multiple reflected lights and the propagation direction of thereflected light from the surface to be measured can be shifted. In thisexample, by utilizing this fact, the influence of the multiple reflectedlights is removed from the recording hologram by performing spatialfiltering in the real space.

The resolution of surface shape measurement is determined by thebandwidth of spatial frequency filtering performed on the reconstructedobject light. The measurement result of FIG. 16A shows the heightdistributions obtained with two kinds of resolutions, high resolutionδ=33 μm and low resolution δ=530 μm. The measurement result of FIG. 16Bis also the same.

In addition to scattered lights due to the surface roughness of thesurface to be measured, scattered lights generated on the surface of thecube-type beam splitter and the cover glass of the image sensor, andnoise generated by the image sensor could be involved in thehigh-frequency component of the height distribution. It is believed thatin order to achieve high accuracy in surface shape measurement andsurface roughness measurement, it is necessary to remove scattered lightgenerated on the beam splitter surface and the cover glass surface.

Example 4

The flatness measurement of the example 4 is described with reference toFIG. 17, FIG. 18A and FIG. 18B. Using the negative pattern USAF testtarget as a sample for surface shape measurement and using the deviceused in the example 1, the complex amplitude inline hologram for shapemeasurement was obtained.

FIG. 17 shows the two-dimensional distribution of heights on the targetsurface. The measurement area is 15 mm×15 mm, and the high partrepresents the chromium surface and the low part represents the surfaceof the glass substrate. The resolution of surface shape measurement isdetermined by the bandwidth of spatial frequency filtering performed onthe reconstructed object light. The resolution of the image shown inFIG. 17 is about 24 μm.

FIG. 18A and FIG. 18B show the height distributions on the straightlines in the x-axis and y-axis directions shown in FIG. 17,respectively. The glass surface and the chrome surface can be clearlydistinguished. The chrome thickness is constant over the entiremeasuring area, and its value is about 60 nm. Further, the results ofFIG. 17 to FIG. 18B show that the glass substrate is curved in a gentlesaddle shape. About 500 m is obtained as the radius of curvature in eachof the x-axis and y-axis directions.

Example 5

The flatness measurement of the example 4 is described with reference toFIG. 19 to FIG. 23. In this example 5, the surface shape measurement wasperformed on a color filter for a liquid crystal display using thesurface shape measuring device 1 according to the 5th embodiment. Thesurface shape measuring device 1 is a device capable of one-shotrecording and measurement with single-wavelength light andtwo-wavelength light. The color filter to be measured has a structure inwhich an RGB filter is attached to a black matrix, and columnar photospacers having a height of about 4 μm and a diameter of about 6 μm arearranged in an equally spaced staggered manner on the color filter.

In the present example, two types of measurement were performed, thatis, measurement with two-wavelength laser lights having wavelengthsλ=756 nm and 786 nm for measuring the height of the columnarphoto-spacer, and measurement with a single wavelength He—Ne laser lighthaving a wavelength λ=632.8 nm for measuring the height of the lowerportion.

FIG. 19 shows the measurement result of the height distribution of thecolor filter in the area of 4 mm in diameter, and FIG. 20 shows anenlarged view of the square portion in FIG. 19. In these images, theportion where the height of the color filter being low is black and theportion where the color filter being high is white, but the columnarphoto spacer a is shown by a black dot for easy viewing. As shown inthese images, the image without distortion can be obtained, and the finestructure of the color filter and the height distribution of each partcan be clearly identified. In addition, the measurement results showthat the flatness of the filter is maintained with extremely highaccuracy.

FIG. 21 shows the measurement result along the straight line (i) in thex-axis direction in FIG. 20, and FIG. 22 shows the measurement resultalong the straight line (ii) in the y-axis direction in FIG. 20. On eachof the straight lines (i) and (ii), two columnar photo spacers a areincluded.

In FIG. 21 and FIG. 22, the filter portions b and c (low peaks withshort cycle) are the results of measurement using laser light having awavelength Δ=632.8 nm, and the photo spacer a (high peaks with longcycle) is the result of measurement using laser light having wavelengthsof Δ=756 nm and 786 nm. The beat wavelength λ_(B) created by the lattertwo laser beams is λ_(B)=19.8 μm, which enables the measurement of thecolumnar photo-spacer a having a height of about 4 μm. A broken lineextending downward from the peak of the photo spacer a indicates aportion where the light intensity of the reconstructed light is toosmall to measure accurately. This indicates that the reflected lightfrom the side of the photo spacer did not reach the image sensor (CCD).

FIG. 23 shows the measurement results side by side with numbers assignedto the photo spacers in the recorded area. From this measurement result,it can be seen that a uniform photo spacer having a height of 4 μm isformed with high accuracy, and useful measurement can be performed. Fromthe results of this example, it is understood that the surface shapemeasuring device 1 and the method according to the 5th embodiment canperform highly accurate height distribution measurement over a widerange from nm to several tens of μm. Further, in the present embodiment,the object light is recorded by one-shot and the measurement result isobtained by the post-processing in the computer, and it can be seen thathigh-speed and highly accurate shape measurement can be realized.

Note that the present invention is not limited to the aboveconfiguration, and various modifications can be made. For example, theconfigurations of the above-described embodiments may be combined witheach other.

INDUSTRIAL APPLICABILITY

The novelty and superiority of the present invention over the prior artinclude: (1) one-shot recording of light waves enables high-speedmeasurement; (2) high-accuracy absolute flatness measurement of thesurface to be measured is possible; (3) since no reference plane orcollimating lens is used, the diameter of the flatness measurement areacan be increased; (4) the flatness measurement can be performed on thesurface to be measured having a wide range of reflection coefficient;(5) the reflected light on the surface to be measured is reconstructedon the surface to be measured, and the reconstructed light can be usedto measure the surface shape and surface roughness with high resolution;(6) adjustment mechanism for movement and rotation is unnecessary, andthe configuration of the recording optical system is very simple.

Due to the above advantages, the present invention can be applied to awide range of applications that make use of these advantages in thefields of optics, digital holography, optical measurement,interferometry, and fine shape measurement. Further, from the viewpointof technological application, it can be considered to be used in fieldssuch as precision measurement, nanotechnology, substrate shapemeasurement, semiconductor substrate inspection, and optical componentinspection. Specific examples of use include surface shape measurementof thin glass substrates, photo-masks, large wafers, etc., surface shapemeasurement of optical parts, measurement of industrial referenceplanes, and the like.

EXPLANATIONS OF LETTERS OR NUMERALS

-   -   1 Surface shape measuring device    -   10 Data acquisition unit    -   12 Image reconstruction unit    -   13 Complex amplitude hologram generation unit    -   14 Calculation reference light hologram generation unit    -   15 Object light hologram generation unit    -   16 Reconstructed object optical hologram generation unit    -   17 Reference point detection unit    -   18 Analytical light hologram generation unit    -   19 Shape measuring unit    -   2 Optical system    -   27 Condenser lens    -   27 a Pupil plate    -   27 b Imaging lens    -   28 Concave mirror    -   28 a Pupil plate    -   28 b Imaging lens    -   3 Beam coupler (cube-type beam splitter)    -   4 Object    -   5 Image sensor    -   50 Hologram plane    -   6 Data storage unit    -   7 Sample stage    -   C Correlation function    -   HW Modulated wave    -   I_(LR), I^(j) _(LR) Reference light off-axis hologram    -   I_(OR), I^(j) _(OR) Object light off-axis hologram    -   J_(OL) Complex-amplitude inline hologram of object light    -   J^(V) _(OS), J_(j) ^(V) _(OS) Measurement hologram (complex        amplitude inline hologram for measurement)    -   L Inline spherical wave reference light    -   Object light    -   P_(L) Condensing point of in-line spherical wave reference light    -   P_(O) Base point    -   P_(R) Condensing point of off-axis reference light    -   Q Illumination light    -   R Off-axis reference light    -   S1 Reference point for shape measurement (reference point light        source)    -   VP Virtual plane    -   fp Virtual point light source (probe function)    -   g Object light hologram    -   h0 Evaluation hologram    -   h^(V) Reconstructed object light hologram    -   j_(L) Inline reference light hologram    -   s^(V) Spherical wave light hologram    -   α_(O) Tilt angle    -   ρ Distance from the image sensor to the condensing point of        inline spherical wave reference light    -   λ_(B) Modulated wavelength    -   λ_(j), λ₁, λ₂ Wavelength    -   θ_(B) Modulated phase

1. A surface shape measuring device using holography, comprising: a dataacquisition unit for acquiring data of an object light (O) that is areflected light of a spherical wave illumination light (Q) illuminatinga surface to be measured and data of an inline spherical wave referencelight (L) that is inline with respect to the object light (O),respectively, as an object light off-axis hologram (I_(OR)) and anreference light off-axis hologram (I_(LR)), using an image sensor; andan image reconstruction unit for deriving data of surface shape byreconstructing an image of the surface to be measured from the dataacquired by the data acquisition unit, wherein the data acquisition unitcomprises: an optical system which is configured to make both anillumination light condensing point (P_(Q)) being a condensing point ofthe spherical wave illumination light (Q) and a reference lightcondensing point (P_(L)) being a condensing point of the inlinespherical wave reference light (L) be arranged in a mirror image of eachother with respect to a virtual plane (VP) being virtually set so as tocontact the surface to be measured, and configured to make the inlinespherical wave reference light (L) obliquely pass through the virtualplane (VP) and enter the image sensor, and the image reconstruction unitcomprises: an object light hologram generation unit for generating anobject light hologram (g) representing the light wave of the objectlight (O) by a calculation process using the data of the two kinds ofoff-axis holograms (I_(OR), I_(LR)), position information of thereference light condensing point (P_(L)), and the fact that the lightemitted from the reference light condensing point (P_(L)) is a sphericalwave; a reconstructed object light hologram generation unit forgenerating a reconstructed object light hologram (h^(V)) on the virtualplane (VP) by performing a light wave propagation calculation and arotational transformation on the object light hologram (g); a referencepoint detection unit for detecting, by performing a light wavepropagation calculation on the object light hologram (g), a position atwhich the object light (O) is condensing, and for setting the positionas a reference point (S1), to be used for shape measurement, having moreprecise information than the position information of the reference lightcondensing point (P_(L)); an analytical light hologram generation unitfor analytically generating a spherical wave light hologram (s^(V)) thatis a hologram, on the virtual plane (VP), of a spherical wave lightemitted from the reference point (S1); and a shape measuring unit forgenerating a measurement hologram (J^(V) _(OS)=h^(V)/s^(V)) by dividingthe reconstructed object light hologram (h^(V)) by the spherical wavelight hologram (s^(V)), and for obtaining a height distribution of thesurface to be measured of the object using a phase distribution of themeasurement hologram (J^(V) _(OS)).
 2. The surface shape measuringdevice according to claim 1, wherein the data acquisition unit comprisesa beam coupler, consisting of a cube-type beam splitter and arrangedimmediately in front of the image sensor, for coupling the off-axisreference light (R), used for acquiring the two kinds of off-axisholograms (I_(OR), I_(LR)), and the object light (O) or the inlinespherical wave reference light (L) so as to make the coupled lightsenter the image sensor, the image reconstruction unit generates, througha calculation process, an inline reference light hologram (j_(L)) whichrepresents a light wave corresponding to the inline spherical wavereference light (L) reaching a hologram plane being a light-receivingsurface of the image sensor after emitted from the reference lightcondensing point (P_(L)) and passing through the beam coupler, byperforming a light wave propagation calculation on a light passingthrough the beam coupler by a plane wave expansion method inconsideration of a refractive index of the beam coupler.
 3. The surfaceshape measuring device according to claim 1, wherein the optical systemcomprises: a condenser lens for condensing the object light (O) and theinline spherical wave reference light (L); a pupil plate being disposedat a condensing position made by the condenser lens to limit amount ofpassing light; and an imaging lens arranged in combination with thepupil plate, so that each image of the object light (O) and the inlinespherical wave reference light (L) is made on the image sensor.
 4. Thesurface shape measuring device according to claim 1, wherein the opticalsystem comprises: a concave mirror for condensing the object light (O)and the inline spherical wave reference light (L); a pupil plate beingdisposed at a condensing position made by the concave mirror to limitamount of passing light; and an imaging lens arranged in combinationwith the pupil plate, so that each image of the object light (O) and theinline spherical wave reference light (L) is made on the image sensor.5. A surface shape measuring method using holography, comprising thesteps of: arranging a reference light condensing point (P_(L)) being acondensing point of an inline spherical wave reference light (L) on anoptical axis of an image sensor, arranging an illumination lightcondensing point (P_(Q)) being a condensing point of a spherical waveillumination light (Q) off the optical axis, and setting a virtual plane(VP) being a plane that bisects a line segment connecting the referencelight condensing point (P_(L)) and the illumination light condensingpoint (P_(Q)) vertically; arranging an object so that a surface to bemeasured is in contact with the virtual plane (VP), and acquiring dataof an object light (O) being a reflected light of the spherical waveillumination light (Q) reflected from the surface to be measured as anobject light off-axis hologram (I_(OR)) using the image sensor;acquiring, in a state where the object is not arranged, data of theinline spherical wave reference light (L) passing through the virtualplane (VP) and being incident on the image sensor as a reference lightoff-axis hologram (I_(LR)) using the image sensor; generating a complexamplitude inline hologram (J_(OL)) containing information on both theobject light (O) and the inline spherical wave reference light (L) fromthe data of the two kinds of off-axis holograms (I_(OR), I_(LR));generating an inline reference light hologram (j_(L)) representing alight wave of the inline spherical wave reference light (L) on ahologram plane being a light-receiving surface of the image sensor byperforming a calculation process using the fact that the inlinespherical wave reference light (L) is a spherical wave light; generatingan object light hologram (g) representing a light wave of the objectlight (O) using the complex amplitude inline hologram (J_(OL)) and theinline reference light hologram (j_(L)); generating a reconstructedobject light hologram (h^(V)) on the virtual plane (VP) by performing alight wave propagation calculation and a rotational transformation onthe object light hologram (g); detecting, by performing a light wavepropagation calculation on the object light hologram (g), a position atwhich the object light (O) is condensing, and setting the position as areference point (S1), to be used for shape measurement, having moreprecise information than the position information of the reference lightcondensing point (P_(L)); generating a spherical wave light hologram(s^(V)) being a hologram on the virtual plane (VP) of a spherical wavelight emitted from the reference point (S1); and generating ameasurement hologram (J^(V) _(OS)=h^(V)/s^(V)) by dividing thereconstructed object light hologram (h^(V)) by the spherical wave lighthologram (s^(V)), and obtaining a height distribution of the surface tobe measured of the object using a phase distribution of the measurementhologram (J^(V) _(OS)).
 6. The surface shape measuring method accordingto claim 5, further comprising the steps of: acquiring, by using lightsof different wavelengths (λ_(j), j=1, 2), the data of the object light(O) and the inline spherical wave reference light (L) as the two kindsof off-axis holograms (I^(j) _(OR), I^(j) _(LR), j=1, 2) for each of thewavelengths (λ₁, λ₂); generating the measurement hologram (J_(j) ^(V)_(OS)=h_(j) ^(V)/s_(j) ^(V), j=1, 2) for each of the wavelengths (λ₁,λ₂); generating a modulated wave (HW=J₁ ^(V) _(OS)/J₂ ^(V) _(OS)) beinga result of a heterodyne conversion for obtaining a ratio of the twomeasurement holograms (J_(j) ^(V) _(OS), j=1, 2); obtaining a heightdistribution of the surface to be measured of the object using amodulated wavelength (λ_(B)=λ₁λ₂/(λ₂−λ₁)) and a modulated phasedistribution (θ_(B)(x′, y)=θ₁−θ₂) which are included in the modulatedwave (HW).
 7. The surface shape measuring method according to claim 5,wherein a sample stage is used to arrange the object so that the surfaceto be measured contacts the virtual plane (VP), adjustment of the samplestage comprises the steps of: fixing a reference plane substrate havinga reference plane on the sample stage, and acquiring data of a reflectedlight from the reference plane substrate as the object light off-axishologram (I_(OR)); generating the complex amplitude inline hologram(J_(OL)) using the object light off-axis hologram (I_(OR)) and thereference light off-axis hologram (I_(LR)); and changing position andtilt of the sample stage so that changes in a phase distribution of thecomplex amplitude inline hologram (J_(OL)) is reduced.
 8. The surfaceshape measuring method according to claim 5, further comprising thesteps of: generating an evaluation hologram (h0) made by propagating theobject light hologram (g) to a position (z=ρ) of the reference lightcondensing point (P_(L)) by performing a light wave propagationcalculation; detecting a position (x1, y1, ρ), where the object light(O) is condensed, in a plane of the evaluation hologram (h0) and settingthe position (x1, y1, ρ) to be a temporary condensing point (P1), bycalculating a correlation function between a probe function (fp)representing a point light source and the evaluation hologram (h0);propagating the evaluation hologram (h0) tentatively in a direction ofthe optical axis by a light wave propagation calculation, performing thecorrelation function calculation while fixing the position of thetemporary condensing point (P1) in the plane of the evaluation hologram(h0), detecting a position (x1, y1, z1) in the direction of the opticalaxis where the object light (O) is condensing, and setting the detectedposition to be the reference point (S1) for the shape measurement. 9.The surface shape measuring device according to claim 2, wherein theoptical system comprises: a condenser lens for condensing the objectlight (O) and the inline spherical wave reference light (L); a pupilplate being disposed at a condensing position made by the condenser lensto limit amount of passing light; and an imaging lens arranged incombination with the pupil plate, so that each image of the object light(O) and the inline spherical wave reference light (L) is made on theimage sensor.
 10. The surface shape measuring device according to claim2, wherein the optical system comprises: a concave mirror for condensingthe object light (O) and the inline spherical wave reference light (L);a pupil plate being disposed at a condensing position made by theconcave mirror to limit amount of passing light; and an imaging lensarranged in combination with the pupil plate, so that each image of theobject light (O) and the inline spherical wave reference light (L) ismade on the image sensor.
 11. The surface shape measuring methodaccording to claim 6, wherein a sample stage is used to arrange theobject so that the surface to be measured contacts the virtual plane(VP), adjustment of the sample stage comprises the steps of: fixing areference plane substrate having a reference plane on the sample stage,and acquiring data of a reflected light from the reference planesubstrate as the object light off-axis hologram (I_(OR)); generating thecomplex amplitude inline hologram (J_(OL)) using the object lightoff-axis hologram (I_(OR)) and the reference light off-axis hologram(I_(LR)); and changing position and tilt of the sample stage so thatchanges in a phase distribution of the complex amplitude inline hologram(J_(OL)) is reduced.
 12. The surface shape measuring method according toclaim 11, further comprising the steps of: generating an evaluationhologram (h0) made by propagating the object light hologram (g) to aposition (z=ρ) of the reference light condensing point (P_(L)) byperforming a light wave propagation calculation; detecting a position(x1, y1, ρ), where the object light (O) is condensed, in a plane of theevaluation hologram (h0) and setting the position (x1, y1, ρ) to be atemporary condensing point (P1), by calculating a correlation functionbetween a probe function (fp) representing a point light source and theevaluation hologram (h0); propagating the evaluation hologram (h0)tentatively in a direction of the optical axis by a light wavepropagation calculation, performing the correlation function calculationwhile fixing the position of the temporary condensing point (P1) in theplane of the evaluation hologram (h0), detecting a position (x1, y1, z1)in the direction of the optical axis where the object light (O) iscondensing, and setting the detected position to be the reference point(S1) for the shape measurement.
 13. The surface shape measuring methodaccording to claim 6, further comprising the steps of: generating anevaluation hologram (h0) made by propagating the object light hologram(g) to a position (z=ρ) of the reference light condensing point (P_(L))by performing a light wave propagation calculation; detecting a position(x1, y1, ρ), where the object light (O) is condensed, in a plane of theevaluation hologram (h0) and setting the position (x1, y1, ρ) to be atemporary condensing point (P1), by calculating a correlation functionbetween a probe function (fp) representing a point light source and theevaluation hologram (h0); propagating the evaluation hologram (h0)tentatively in a direction of the optical axis by a light wavepropagation calculation, performing the correlation function calculationwhile fixing the position of the temporary condensing point (P1) in theplane of the evaluation hologram (h0), detecting a position (x1, y1, z1)in the direction of the optical axis where the object light (O) iscondensing, and setting the detected position to be the reference point(S1) for the shape measurement.
 14. The surface shape measuring methodaccording to claim 7, further comprising the steps of: generating anevaluation hologram (h0) made by propagating the object light hologram(g) to a position (z=ρ) of the reference light condensing point (P_(L))by performing a light wave propagation calculation; detecting a position(x1, y1, ρ), where the object light (O) is condensed, in a plane of theevaluation hologram (h0) and setting the position (x1, y1, ρ) to be atemporary condensing point (P1), by calculating a correlation functionbetween a probe function (fp) representing a point light source and theevaluation hologram (h0); propagating the evaluation hologram (h0)tentatively in a direction of the optical axis by a light wavepropagation calculation, performing the correlation function calculationwhile fixing the position of the temporary condensing point (P1) in theplane of the evaluation hologram (h0), detecting a position (x1, y1, z1)in the direction of the optical axis where the object light (O) iscondensing, and setting the detected position to be the reference point(S1) for the shape measurement.